Prove that this law is as stated. Determine the approximate values of k and n, and hence state the law.

Consider

Take the log (or natural log, or log to your favorite base, whatever) of both sides:

What does this do for you? Well the equation is now in the form
where

So what you do is a linear regression with the log(L) values being your x values and the log(T) values being the y values. Then the slope m of the regression will be n, and the intercept b will be the log(k).

Edit: For reference I get that and with an , so the fit for is excellent. This is not quite the same as Soroban's answer (which is easier to get) but is probably more accurate. (Sorry Soroban, I'm not trying to pick on your answer! :) )

-Dan

Aug 4th 2007, 06:50 AM

Soroban

Hello, Dean!

Quote:

The table below gives values of and
which are related by the law where and are constants.

Prove that this law is as stated.
Determine the approximate values of and , and hence state the law.